Preheat oven to 350 degrees F (175 degrees C). Grease a 12-cup muffin pan.
Stir oats and milk together in a small bowl; set aside.
Whisk flour, white sugar, baking powder, baking soda, and salt together in a large bowl. Whisk vegetable oil and egg together in a separate bowl; stir egg mixture into flour mixture just until batter is combined.
Fold oat mixture into batter; fold in saskatoon berries. Divide batter evenly into the prepared muffin cups; sprinkle muffins with brown sugar.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 18 minutes. Cool in pans 10 minutes. Serve warm or cool completely on a wire rack.
